Abstracts of Invited Speakers

s of Invited Speakers Teaching mathematics in context as a social construct H Barnes, University of Pretoria Why is teaching in context a necessary option to consider in the teaching of mathematics? What does it mean to teach mathematics from and in contexts? And what are the possible challenges associated with this practice? The aim of this paper is to attempt to address these questions from literature and data from a developmental research project carried out using the theory of Realistic Mathematics Education. The philosophical shift that has occurred within the domain of mathematics has brought with it a wave of reform in mathematics education. The former absolutist paradigm that dominated undermined the social responsibility of mathematics in human affairs such as value, wealth and power (Ernest, 1991). The shift has challenged the infallibility of mathematics and acknowledged it as a product of human inventiveness (Davis and Hersh, 1980) and a human activity (Freudenthal, 1973), thus making it a social construct. While the reform propagating the teaching of mathematics as a social construct is a positive move, along with the introduction of mathematical literacy in many countries, how can we effectively implement this reform? This paper seeks to examine the area of teaching mathematics in context to support this reform and how we can consider implementing this in both school and tertiary education. Mathematicians and Fisheries Management: a Marriage of Opportunism or Necessity? Doug S Butterworth, MARAM (Marine Resource Assessment and Management Group), Department of Mathematics and Applied Mathematics, University of Cape Town For perspective, first a brief summary is given on how the commercial fisheries of South Africa and Namibia contribute to fishing worldwide and to local economies. The fundamental (and conflicting) objectives of fisheries management are explained, together with the key role of mathematical analysis in quantifying the trade-offs between them. This includes a short account of the basic process of resource assessment (what data are typically used in an integrative mathematical process to estimate the size and productivity of a fish population), together with the control rules applied to such results to set catch limits in a feedback manner that aims to move the population to a desired size. The critical need to deal with difficulties arising because of uncertainties, related both to poor statistical precision and to model structure, is emphasised. An account is given of the developing Management Procedure simulation-testing approach (in which South Africa has played a pioneering role) that aims to provide robust attainment of objectives in these circumstances. The example of South Africas most important fishery (that for hake) is used to illustrate how this approach is being applied at the moment to select between options to achieve an economically essential improvement in catch rates. Reference is also made to aspects of analysis for the major local fishery for the small near-surface shoaling species, sardine and anchovy, which is complicated by the unavoidable catch of juveniles of the former in hauls targeted at the latter, and for abalone where estimation of the substantial level of poaching is an essential component. Results are shown of attempts to apply species interaction models to explain the trends of the main whale and seal species around Antarctica following their heavy exploitation and subsequent protection. Finally some comments on the current state of the marriage: improving with age, or headed towards the divorce courts?